Excitation conditions for quantitative determination of quadrupolar spins with one pulse or spin-echo sequences in solid-state NMR

Abstract

One of the major problems concerning quadrupolar spins in solid-state NMR is their quantification. If the optimal excitation conditions with one radio-frequency pulse are widespread known now, this is not the case with the spin-echo sequences. This paper reports some theoretical predictions and their limitations concerning quantification with the echo obtained with spin-echo resonances. To realize that, first, the relative line intensity of a transition (m+1,m) is defined in order to allow the comparison of results, from different authors. Then results concerning one pulse excitation on a spinI=3/2 are summarized. The condition of short pulse excitation is generalized to higher spins using the Pauli matrices applied to the two extreme cases: hard pulse or non selective excitation, and selective excitation. Finally the same procedure has been followed for the spin-echo sequence involving twox-pulses. It was shown that the optimum conditions are: both the pulse length must be sufficiently short, and the interpulse delay should be taken as short as the duration of the FID provided the phase of the second pulse alternates without changing the receiver phase. In these conditions, the relative echo amplitude depends linearly on the first pulse length and quadratically on the second. The limitations are: the homonuclear magnetic dipolar interaction must be much smaller than the heteronuclear case which must be itself much smaller than the amplitude of the pulse. Furthermore, quantification with the echo requires the determination of the spin-spin relaxation time as well.